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1.11.5 Integration by substitution and by parts (A-level only)

1.11.5 Integration by substitution and by parts (A-level only)

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Question 62

A high-precision sensor measures the rate of energy dissipation, R(t)R(t)R(t), in a prototype circuit over the interval 0≤t≤π60 \le t \le \frac{\pi}{6}0≤t≤6π​ seconds. The rate is modeled by the function:

R(t)=(3t−1)cos⁡(3t) R(t) = (3t - 1) \cos(3t) R(t)=(3t−1)cos(3t)

Given that the total energy dissipated, E=∫0π6R(t) dtE = \int_{0}^{\frac{\pi}{6}} R(t) \, dtE=∫06π​​R(t)dt, can be expressed in the form aπ+ba\pi + baπ+b, find the exact value of aaa and the exact value of bbb.

Fully justify your answer.

[6]
Markscheme

1.11.5 Integration by substitution and by parts (A-level only) Questions

  1. A Level
  2. /Maths
  3. /1.11.5 Integration by substitution and by parts (A-level only)

119 exam-style questions on AQA A Level Maths 1.11.5 Integration by substitution and by parts (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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